Pith Number

pith:6CHA4PAK

pith:2006:6CHA4PAK4I46PFOZWWYLV3L2GJ

not attested not anchored not stored refs pending

The random paving property for uniformly bounded matrices

Joel A. Tropp

arxiv:math/0612070 v5 · 2006-12-04 · math.MG · math.FA · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6CHA4PAK4I46PFOZWWYLV3L2GJ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T02:53:05.103049Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f08e0e3c0ae239e795d9b5b0baed7a326cbddfb24c60ce7930aac0a4265e7af1

Aliases

arxiv: math/0612070 · arxiv_version: math/0612070v5 · doi: 10.48550/arxiv.math/0612070 · pith_short_12: 6CHA4PAK4I46 · pith_short_16: 6CHA4PAK4I46PFOZ · pith_short_8: 6CHA4PAK

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/6CHA4PAK4I46PFOZWWYLV3L2GJ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: f08e0e3c0ae239e795d9b5b0baed7a326cbddfb24c60ce7930aac0a4265e7af1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d20bfe66dd24ef87da12c90f2e899f5d46054eca4794e02cffbc1b48a9553380",
    "cross_cats_sorted": [
      "math.FA",
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math.MG",
    "submitted_at": "2006-12-04T00:33:57Z",
    "title_canon_sha256": "610935b1ba1810cfba7879c1ede5c56615233a7aa6fdd116fcc8baf526cede37"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0612070",
    "kind": "arxiv",
    "version": 5
  }
}